%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYN997^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 11:07:20 AM UTC 2026
% Result : Theorem 0.08s 0.21s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 1
% Syntax : Number of formulae : 24 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 102 ( 27 equ; 0 cnn)
% Maximal formula atoms : 2 ( 4 avg)
% Number of connectives : 158 ( 31 ~; 10 |; 2 &; 111 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 46 ( 46 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 36 ( 0 ^; 28 !; 8 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_sK1_P,type,
sK1_P: ( ( $i > $o ) > $i ) > $i > $o ).
thf(tp_sK2_SY3,type,
sK2_SY3: ( ( $i > $o ) > $i ) > $i ).
thf(tp_sK3_Eigen,type,
sK3_Eigen: ( $i > $o ) > $i ).
thf(1,conjecture,
? [E: ( $i > $o ) > $i] :
! [P: $i > $o] :
( ? [Y: $i] : ( P @ Y )
=> ( P @ ( E @ P ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
( ( ? [E: ( $i > $o ) > $i] :
! [P: $i > $o] :
( ? [Y: $i] : ( P @ Y )
=> ( P @ ( E @ P ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ? [E: ( $i > $o ) > $i] :
! [P: $i > $o] :
( ? [Y: $i] : ( P @ Y )
=> ( P @ ( E @ P ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ~ ? [E: ( $i > $o ) > $i] :
! [P: $i > $o] :
( ? [Y: $i] : ( P @ Y )
=> ( P @ ( E @ P ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [E: ( $i > $o ) > $i] :
( ( sK1_P @ E @ ( sK2_SY3 @ E ) )
& ~ ( sK1_P @ E @ ( E @ ( sK1_P @ E ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [E: ( $i > $o ) > $i] :
( ( sK1_P @ E @ ( sK2_SY3 @ E ) )
& ~ ( sK1_P @ E @ ( E @ ( sK1_P @ E ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [SX0: ( $i > $o ) > $i] :
~ ( ~ ( sK1_P @ SX0 @ ( sK2_SY3 @ SX0 ) )
| ~ ~ ( sK1_P @ SX0 @ ( SX0 @ ( sK1_P @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(8,plain,
! [SV1: ( $i > $o ) > $i] :
( ( ~ ( ~ ( sK1_P @ SV1 @ ( sK2_SY3 @ SV1 ) )
| ~ ~ ( sK1_P @ SV1 @ ( SV1 @ ( sK1_P @ SV1 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7]) ).
thf(9,plain,
! [SV1: ( $i > $o ) > $i] :
( ( ~ ( sK1_P @ SV1 @ ( sK2_SY3 @ SV1 ) )
| ~ ~ ( sK1_P @ SV1 @ ( SV1 @ ( sK1_P @ SV1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[8]) ).
thf(10,plain,
! [SV1: ( $i > $o ) > $i] :
( ( ~ ( sK1_P @ SV1 @ ( sK2_SY3 @ SV1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[9]) ).
thf(11,plain,
! [SV1: ( $i > $o ) > $i] :
( ( ~ ~ ( sK1_P @ SV1 @ ( SV1 @ ( sK1_P @ SV1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[9]) ).
thf(12,plain,
! [SV1: ( $i > $o ) > $i] :
( ( sK1_P @ SV1 @ ( sK2_SY3 @ SV1 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[10]) ).
thf(13,plain,
! [SV1: ( $i > $o ) > $i] :
( ( ~ ( sK1_P @ SV1 @ ( SV1 @ ( sK1_P @ SV1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[11]) ).
thf(14,plain,
! [SV1: ( $i > $o ) > $i] :
( ( sK1_P @ SV1 @ ( SV1 @ ( sK1_P @ SV1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(15,plain,
( ( sK1_P @ sK3_Eigen @ ( sK3_Eigen @ ( sK1_P @ sK3_Eigen ) ) )
= $false ),
inference(instantiate,[status(thm)],[14:[bind(SV1,$thf( sK3_Eigen ))]]) ).
thf(16,plain,
! [SV1: ( $i > $o ) > $i] :
( ( ~ ~ ! [SV2: $i] :
~ ( sK1_P @ SV1 @ SV2 )
| ( sK1_P @ SV1 @ ( sK3_Eigen @ ( sK1_P @ SV1 ) ) ) )
= $true ),
inference(choice,[status(thm)],[14]) ).
thf(17,plain,
! [SV3: ( $i > $o ) > $i] :
( ( ~ ~ ! [SX0: $i] :
~ ( sK1_P @ SV3 @ SX0 )
| ( sK1_P @ SV3 @ ( sK3_Eigen @ ( sK1_P @ SV3 ) ) ) )
= $true ),
inference(rename,[status(thm)],[16]) ).
thf(18,plain,
! [SV3: ( $i > $o ) > $i] :
( ( ( ~ ~ ! [SX0: $i] :
~ ( sK1_P @ SV3 @ SX0 ) )
= $true )
| ( ( sK1_P @ SV3 @ ( sK3_Eigen @ ( sK1_P @ SV3 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[17]) ).
thf(19,plain,
! [SV3: ( $i > $o ) > $i] :
( ( ( ~ ! [SX0: $i] :
~ ( sK1_P @ SV3 @ SX0 ) )
= $false )
| ( ( sK1_P @ SV3 @ ( sK3_Eigen @ ( sK1_P @ SV3 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(20,plain,
! [SV3: ( $i > $o ) > $i] :
( ( ( ! [SX0: $i] :
~ ( sK1_P @ SV3 @ SX0 ) )
= $true )
| ( ( sK1_P @ SV3 @ ( sK3_Eigen @ ( sK1_P @ SV3 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[19]) ).
thf(21,plain,
! [SV4: $i,SV3: ( $i > $o ) > $i] :
( ( ( ~ ( sK1_P @ SV3 @ SV4 ) )
= $true )
| ( ( sK1_P @ SV3 @ ( sK3_Eigen @ ( sK1_P @ SV3 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(22,plain,
! [SV4: $i,SV3: ( $i > $o ) > $i] :
( ( ( sK1_P @ SV3 @ SV4 )
= $false )
| ( ( sK1_P @ SV3 @ ( sK3_Eigen @ ( sK1_P @ SV3 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(23,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[12,22,15,14]) ).
thf(24,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN997^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.17 % Computer : n002.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Oct 6 17:33:27 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.21
% 0.08/0.21 No.of.Axioms: 0
% 0.08/0.21
% 0.08/0.21 Length.of.Defs: 0
% 0.08/0.21
% 0.08/0.21 Contains.Choice.Funs: false
% 0.08/0.21
% 0.08/0.21 *** Modified list of choice operators: sK3_Eigen ***
% 0.08/0.21
% 0.08/0.21 ********************************
% 0.08/0.21 * All subproblems solved! *
% 0.08/0.21 ********************************
% 0.08/0.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:23,loop_count:0,foatp_calls:2,translation:fof_experiment)
% 0.08/0.21
% 0.08/0.21 %**** Beginning of derivation protocol ****
% 0.08/0.21 % SZS output start CNFRefutation
% See solution above
% 0.08/0.21
% 0.08/0.21 %**** End of derivation protocol ****
% 0.08/0.21 %**** no. of clauses in derivation: 24 ****
% 0.08/0.21 %**** clause counter: 23 ****
% 0.08/0.21
% 0.08/0.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:23,loop_count:0,foatp_calls:2,translation:fof_experiment)
%------------------------------------------------------------------------------